Finite Group Databasebeta

← #11775326

Subgroups — #11775326

Order 1152.

596 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic
2#10593811C211yesmaximal, characteristic
3#10593803C211yesmaximal, characteristic
4#10590215C212yesmaximal, complemented
5#10590158C212yesmaximal, complemented
6C2×Q8×C3⋊D3C411yescharacteristic, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×#3788—21no—
10C32×C22⋊Q8C411yescharacteristic, complemented
11#64155C2211yescharacteristic
12#64133C411yescharacteristic, complemented
13#64106C2211yescharacteristic
14#64105—21no—
15C4⋊C4×C3⋊D3—21no—
16C4⋊C4×C3⋊D3C411yescharacteristic, complemented
17C22⋊C4×C3⋊D3—21no—
18#64087—21no—
19C22⋊#622—21no—
20#63781—21no—
21#63781C2212yes—
22#63778C2212yes—
23D3×C22⋊Q8—62no—
24C23×C3⋊D3D411yescharacteristic
25C22×#157—22no—
26C2×C32×Q8C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29Q8×C3⋊D3—42no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—42no—
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×#634—21no—
38C2×#634C2×C411yescharacteristic
39C22⋊#157—42no—
40C2×#622—22no—
41#3788—42no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4C2×C411yescharacteristic
44C32×C22⋊C4—21no—
45#3757—21no—
46#3752—21no—
47#3752—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)C2×C411yescharacteristic
50#3750—21no—
51#3750—21no—
52#3750—21no—
53#1511—91nomaximal, Sylow
54C2×D3×Q8—62no—
55C22×C4×D3—62no—
56C3×C22⋊Q8—22no—
57#946—62no—
58#924—62no—
59#897—62no—
60#896—64no—
61D3×C4⋊C4—62no—
62D3×C4⋊C4—64no—
63D3×C22⋊C4—64no—
64#878—64no—
65C23×C32C22⋊C411yescharacteristic
66C22×C3⋊D3—22no—
67C22×C3⋊D3—22no—
68C22×C3⋊D3—41no—
69C22×C3⋊D3C22⋊C411yescharacteristic
70C22×C3⋊D3C2×D411yescharacteristic
71C2×#157—42no—
72C2×#157—42no—
73C2×#157—42no—
74C32×Q8—41no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—41no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C2×D411yescharacteristic
85C4×C3⋊D3—22no—
86C4×C3⋊D3—22no—
87C4×C3⋊D3—41no—
88C4×C3⋊D3—41no—
89C4×C3⋊D3—42no—
90C4×C3⋊D3—42no—
91#634—42no—
92#634—41no—
93#622—42no—
94C2×C22⋊Q8—91no—
95#407—91no—
96#381—91no—
97#328—92no—
98#328—92no—
99C23×D3—62no—
100C2×C3×Q8—22no—
101C22×C3×C4—22no—
102C22×Dic3—62no—
103D3×Q8—128no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—62no—
107C2×C4×D3—62no—
108C2×C4×D3—64no—
109C2×C4×D3—64no—
110C2×C4×D3—128no—
111C2×Dic6—62no—
112C2×Dic6—64no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—22no—
115C3×C22⋊C4—24no—
116#217—64no—
117(C2×D3)⋊C4—64no—
118(C2×D3)⋊C4—64no—
119C4⋊Dic3—62no—
120C4⋊Dic3—64no—
121Dic3⋊C4—64no—
122Dic3⋊C4—64no—
123Dic3⋊C4—64no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—21no—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3⋊D3—21no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3—21no—
131C2×C3⋊D3—21no—
132C2×C3⋊D3—44no—
133C2×C3⋊D3#9912yes—
134C2×C3⋊D3#13712yes—
135#157—82no—
136C32×C4—21no—
137C32×C4—21no—
138C32×C4—41no—
139C32×C4—41no—
140C3⋊Dic3—21no—
141C3⋊Dic3—21no—
142C3⋊Dic3—41no—
143C3⋊Dic3—41no—
144C22×Q8—91no—
145C23×C4—91no—
146C2×M16—181no—
147C22⋊Q8—91no—
148C22⋊Q8—91no—
149C22⋊Q8—91no—
150C22⋊Q8—181no—
151C22⋊Q8—181no—
152C22⋊Q8#15711yescharacteristic, complemented
153C2×C4⋊C4—91no—
154C2×C4⋊C4—181no—
155C2×C22⋊C4—181no—
156C2×C22⋊C4—181no—
157C22⋊C8—92no—
158C22⋊C8—181no—
159#95—92no—
160#95—181no—
161C23×C3—22no—
162C22×D3—62no—
163C22×D3—62no—
164C22×D3—68no—
165C22×D3—124no—
166C22×D3—124no—
167C3×Q8—44no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—44no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—124no—
178C4×D3—68no—
179C4×D3—124no—
180C4×D3—124no—
181C4×D3—124no—
182C4×D3—128no—
183C4×D3—128no—
184Dic6—128no—
185Dic6—124no—
186C2×C32—41no—
187C2×C32C2×#9911yescharacteristic
188C2×C32#41911yescharacteristic
189C2×C32#42111yescharacteristic
190C3⋊D3—22no—
191C3⋊D3—22no—
192C24—91no—
193C2×Q8—91no—
194C2×Q8—181no—
195C2×Q8—362no—
196C2×Q8C2×#15711yescharacteristic
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—181no—
203C22×C4—181no—
204C22×C4—182no—
205C22×C4—362no—
206C22×C4C2×#15711yescharacteristic
207M16—362no—
208C2×C8—182no—
209C4⋊C4—21no—
210C4⋊C4—91no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4—181no—
214C4⋊C4—181no—
215C4⋊C4C2×#15711yescharacteristic
216C22⋊C4—21no—
217C22⋊C4—181no—
218C22⋊C4—181no—
219C22⋊C4—181no—
220C22⋊C4—362no—
221C22×C3—24no—
222C22×C3—22no—
223C22×C3—42no—
224C22×C3—42no—
225C2×D3—64no—
226C2×D3—64no—
227C2×D3—64no—
228C2×D3—64no—
229C2×D3—122no—
230C2×D3—122no—
231C2×D3—1216no—
232C3×C4—24no—
233C3×C4—42no—
234C3×C4—44no—
235C3×C4—44no—
236Dic3—64no—
237Dic3—122no—
238Dic3—124no—
239Dic3—124no—
240C32#151111yescharacteristic, complemented, Sylow
241C23—91no—
242C23—91no—
243C23—182no—
244C23—182no—
245C23—361no—
246C23C22⋊#15711yescharacteristic
247Q8—41no—
248Q8—361no—
249Q8—362no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—181no—
258C2×C4—181no—
259C2×C4—361no—
260C2×C4—361no—
261C2×C4—362no—
262C2×C4—362no—
263C2×C4—361no—
264C2×C4—362no—
265C2×C4—362no—
266C2×C4—362no—
267C2×C4C22⋊#15711yescharacteristic
268C2×C4C22×#15711yescharacteristic
269C8—362no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—44no—
274D3—68no—
275D3—124no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—92no—
280C22—92no—
281C22—181no—
282C22—181no—
283C22—181no—
284C22—181no—
285C22—364no—
286C22C2×C22⋊#15711yescharacteristic
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—181no—
292C4—181no—
293C4—361no—
294C4—361no—
295C4—722no—
296C3—22no—
297C2—41no—
298C2—182no—
299C2—182no—
300C2#1059381711yescharacteristic
301C2#1059382911yescharacteristic
302C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22⋊Q8#157
hypocenterC32#1511
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #10590215C2semidirect
5. #10590158C2semidirect
6. C2×Q8×C3⋊D3C4semidirect
10. C32×C22⋊Q8C4semidirect
12. #64133C4semidirect
16. C4⋊C4×C3⋊D3C4semidirect
152. C22⋊Q8#157semidirect
240. C32#1511semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3⋊D3×C22⋊Q82
#105938112
#105938032
#105902152
#105901582
#15119